294 Maxwell. 



The dispersion of light within the limits of the visible 

 spectrum is for most substances controlled by a natural 

 frequency p which corresponds to a vibration beyond the violet 

 end of the visible spectrum : so that, n being smaller than p, 

 we may expand the fraction in the formula of dispersion, and 

 obtain the equation 



(T I n z n* 



fJL 2 = 1 + - (1 + - + -+... 

 f>\ P* P* 



which resembles the formula of dispersion in Cauchy's theory* ; 

 indeed, we may say that Cauchy's formula is the expansion of 

 Maxwell's formula in a series which, as it converges only when 

 n has values within a limited range, fails to represent the 

 phenomena outside that range. 



The theory as given above is defective in that it becomes 

 meaningless when the frequency n of the incident light is 

 equal to the frequency p of the free vibrations of the atoms. 

 This defect may be remedied by supposing that the motion of 

 an atomic particle relative to the shell in which it is contained 

 is opposed by a dissipative force varying as the relative 

 velocity ; such a force suffices to prevent the forced vibration 

 from becoming indefinitely great as the period of the incident 

 light approaches the period of free vibration of the atoms ; its 

 introduction is justified by the fact that vibrations in this 

 part of the spectrum suffer absorption in passing through the 

 medium. When the incident vibration is not in the same 

 region of the spectrum as the free vibration, the absorption is 

 not of much importance, and may be neglected. 



It is shown by the spectroscope that the atomic systems 

 which emit and absorb radiation in actual bodies possess more 

 than one distinct free period. The theory already given may, 

 however, readily be extended-)- to the case in which the atoms 

 have several natural frequencies of vibration ; we have only to 

 suppose that the external massless rigid shell is connected by 

 springs to an interior massive rigid shell, and that this again 

 * Cf. p. 183. 



t This subject was developed by Lord Kelvin in the' Baltimore Lectures. 



